Validation of Advanced Kinematic Model of Earth-Moon System by Observed Length of Day Curve

Abstract

Bijay Kumar Sharma

NASA’s press release of ‘Moon having receded by 1 m from Earth in a quarter of century’ on the Silver Jubilee Anniversary (20 July 1994) of Man’s landing on Moon led to the development of the Kinematic Model(KM) of evolving Earth-Moon System. Best fit KM parameters are adopted for the analysis of evolving E-M system, The present length of day of Earth is assumed to be 24 hours, orbital period of Moon divided by spin period of Earth=LOM/LOD=27.322 and the age of Moon=4.467Gy. Using this best fit model parameters the velocity of recession of Moon is derived as 2.3cm/y as compared to 3.7cm/y by Lunar Laser Ranging experiment.KM is used to plot lengthening of day(LOD) curve from pre-cambrian period (2.5Gy ago) to the present time. This theoretical plot is superimposed on the observed lengthening of day curve. The observed plot is generated from the observed length of day in different geologic epochs by John West Wells, Charles P.Sonnet & Chan and Kaula & Harris by the study of coral fossils, ancient tidalites and marine creatures respectively. The superposition gives more than 25% mismatch in remote past around 2.5Gya. This KM did not consider the obliquity angle 23.44° of Earth and the inclination angle of 5.14° of Lunar Orbital Plane with respect to Ecliptic plane. The classical KM assumed monotonic spiral expansion of Moon from Earth as shown in Figure 1. A recent paper “Tidal evolution of Moon in high angular momentum, high obliquity Earth” has revolutionized the Earth-Moon modeling and paved the way for near-match between observated and theoretical LOD curve. In the new scenario Moon’s tidal evolution is anything but sedate and monotonic. It experienced a bumpy launch through gravitational sling shot at the first geo-synchronous orbit of 15,000Km. Moon was gravitationally catapulted and launched on an expanding spiral path but this expansion was turbulent, chaotic and got stalled at times due to huge lunar obliquity tides during Laplace Plane transition and due to Cassini state transition as shown in Figure 2. Only after Moon settles down in Cassini state II that it resumes its monotonic and sedate spiral expansion as envisaged in the classical picture but this spiral expansion was at accelerated pace so as to reach 3,84,499Km orbital radius in 4.5Gy. It transits in fits , in chaotic and turbulent phase, for 3.3Gy whereas it spends1.2Gy in bounded state therefore this new model is referred to as ‘Fits and Bound’ model of E-M system. On this time scale the modern time recession rate comes to be 3.7cm/y. If this accelerated time frame is adopted then we get near-exact match between theory and observed LOD curve with worst mis-match being -4%. In this accelerated time frame, all E-M system parameters are obtained and it is self consistent model with velocity of recession = 3.7cm/y, LOM/LOD = 27.322 and near match between theory and observed LOD curve and spending 3.3Gy in turbulent and stalled evolutionary phase and spending 1.2Gy in the present accelerated phase. This gives the final vindication to the advanced KM.

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